©2014 IDBS, Confidential
Statistical Process Control
Workshop
An Introduction to the Principles
behind SPC
Ilca Croufer
©2014 IDBS, Confidential
Workshop Outline
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1. Statistical Process Control
a) Definition
b) Benefits & Tools
2. Process
a) Definition
b) Common & Special Cause Variation
3. Statistics Revision
a) Mean, Variance and Standard Deviation
b) Normal Distribution
4. Control Charts
5. Control Chart Construction
6. Examples of Root Cause Analysis Techniques
a) 5 Whys
b) Fishbone Diagram
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©2014 IDBS, Confidential
Statistical Process Control (SPC)
 Statistical process control (SPC) is a methodology focused on quality
control and improvement, using data analysis
 It consists of using valid statistical data analysis to determine and
eliminate variation due to assignable causes.
 It is based on the following principles:
- measuring the process
- identifying and eliminating unusual variation
- improving the process to its best target value
- monitoring the process performance over time
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Benefits of Statistical Process Control
 Process improvement
 In-depth management decision making
 Better understanding of process performance
 Establish process baselines
 Better control on variables that impact a process
 Gain More predictability
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Examples of Tools used in SPC
 Histograms
 Scatter Diagrams
 Run Charts
 Pareto Charts
 Control Charts
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Process & Variation
 An activity which transforms inputs into outputs; (F(x) = Y)
INPUTS
X
ACTIVITY
OUTPUTS
f(X)
Y
Example: making a cup of tea, baking a cake, getting to work, etc.
 Any process will have a certain degree of variation; some variation will be
inherent to the process, some will not.
 Variation in a Process = Common Cause Variation + Special Cause
variation
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Common Cause vs Special Cause Variation
 Common Cause Variation:
- Irregular variation within an historical experience base
- Naturally present within the system
- Usually insignificant and predictable
 Special Cause Variation
- Variation outside the historical experience base
- Assignable to a root cause
- Usually significant and unpredictable
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Statistics Revision I
 Distribution: arrangement of values of a variable showing their observed
or theoretical frequency of occurrence.
E.g.: 21 25 33 33 45 47 51 55 55 61
 A distribution is usually characterised by its mean, standard deviation
and shape
 In Statistics, different types of distribution exist, with the Normal
Distribution being the most well-known and commonly used.
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Statistics Revision II
 Mean =
∑ (sum of observed values)
Number of observations
 Variance =
∑ (observed value – mean)2
Number of observations

Standard Deviation ( ) =
√ (Variance)
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Example II
Consider the following distribution:
11, 17,25, 28, 34
Calculate the mean, variance and standard deviation.
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Example II - Solution
 Mean = (11+17+25+28+34) = 23
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 Variance = (11-23)2+(17-23)2+(25-23)2+(28-23)2+(34-23)2
= 66
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 Standard Deviation = √66 = 8.12
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Exercise I - Solution
 Mean = (1.0+0.8+0.8+1.2) = 0.95
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 Variance = (1.0-0.95)2+(0.8-0.95)2+(0.8-0.95)2+(1.2-0.95)2
= 0.0275
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 Standard Deviation = √0.0275 = 0.17
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Normal Distribution Curve
 Bell-shaped curve
 Symmetrical around the mean
 Defined by its mean and standard deviation
 68.3% of data found within one standard deviations away from the mean
 95.5% of data found within two standard deviations away from the mean
 99.7% of data found within three standard deviations away from the
mean
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Control Charts
 Statistical tool used to
monitor the stability
of a process over time
 Key features:
- UCL (Upper Control Limit) = mean + 3*sigma
- LCL (Lower Control Limit) = mean – 3*sigma
- central line (mean of data set)
 A process is said to be in control when data points fall within limits
of variation (i.e.: between Upper and Lower Control Limits)
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Some Control Chart Rules
 Rule1: Any point falls beyond 3 sigma from the centre line
 Rule2: Two out of three consecutive points fall beyond 2 sigma
on the same side of the centre line
 Rule3: Four out of five consecutive points fall beyond 1 sigma
on the same side of the centre line
 Rule4: Nine or more consecutive points fall on the same side
of the centre line
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Exercise III – Part I
 Consider the next set of control charts and identify whether the process is “incontrol” or “out of control”:
(a)
(b)
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10
8
8
6
6
4
4
2
2
0
0
1
2
3
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11
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2
3
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9
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Data
Mean
UCL
LCL
Data
Mean
UCL
LCL
1 SIGMA
2 SIGMA
-1 SIGMA
-2 SIGMA
1 SIGMA
2 SIGMA
-1 SIGMA
-2 SIGMA
11
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Exercise III – Part II
(c)
(d)
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10
10
8
8
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6
4
4
2
2
0
0
1
2
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2
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Data
Mean
UCL
LCL
Data
Mean
UCL
LCL
1 SIGMA
2 SIGMA
-1 SIGMA
-2 SIGMA
1 SIGMA
2 SIGMA
-1 SIGMA
-2 SIGMA
11
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Type I & Type II Errors
 Type I errors occur when a point falls outside the control limits even
though no special cause is operating.
 Type II errors occur when you miss a special cause because the chart
isn't sensitive enough to detect it
 All process control is vulnerable to these two types of errors.
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Control Charts & Data Types
 Control charts can measure two types of data:
- Continuous Data (can be measured)
E.g.: temperature, volume, weight, height, time
- Discrete Data (can be counted)
E.g.: How many people in this room?
How many defects in an inspected unit?
 There are different control charts to choose from depending on what data
is available.
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Control Chart Types
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Data Collection
 Before assessing the stability of a process over time using control charts,
it is important to identify the type of data at hand, and how to consistently
collect and validate it:
1. Decide what to collect: what metrics?
2. Determine the needed sample size
3. Identify source/location of data
4. Is the data in a useable form?
5. Identify how to collect the data consistently and validate it
6. Decide who will collect the data
7. Consider what you’ll have to do with the data (sorting, graphing,
calculations)
8. Execute your data collection plan
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Root Cause Analysis – 5 Whys
5 Whys: a problem solving tool that helps understand the root cause
of a problem. The 5 Whys technique is usually very quick
and focused.
Key Points:
The 5 Whys strategy is an easy and often-effective tool for
uncovering the root cause of a problem.
Because it's simple, you can adapt it quickly and apply it to
almost any problem.
However, it is important to remember, if an intuitive answer is hard
to find, then other problem-solving techniques may need to be considered.
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©2014 IDBS, Confidential
Root Cause Analysis – Fishbone Diagram
 Fishbone diagrams: diagram-based technique, which combines
brainstorming with a type of mind map, and forces to consider all
possible causes of a problem, rather than just the ones that are most
obvious. Fishbone diagrams encourage broad thinking.
 Key Points:
1. Identify the problem.
2. Work out the major factors involved.
3. Identify possible causes.
4. Analyse your diagram.
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Conclusion
 When used correctly, control charts are powerful
instruments that can give you visual understanding on the
stability of your process
 Control charts cannot tell you what is wrong with your
process, they can only let you know when something in your
process has changed
 Control charts can confirm the impact of process
improvement activities
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©2014 IDBS, Confidential
Thank you for attending
Ilca Croufer
icroufer@idbs.com
2 Occam Court
Surrey Research Park
Guildford, Surrey
GU2 7QB
Tel: +44 1483 595 000
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